Oscillatory-Plus-Transient Signal Decomposition Using TQWT and MCA

Abstract

This paper describes a method for decomposing a signal into the sum of an oscillatory component and a transient component. The process uses the tunable Q-factor wavelet transform (TQWT): The oscillatory component is modeled as a signal that can be sparsely denoted by high Q-factor TQWT; similarly, the transient component is modeled as a piecewise smooth signal that can be sparsely denoted using low Q-factor TQWT. Since the low and high Q-factor TQWT has low coherence, the morphological component analysis (MCA) can effectively decompose the signal into oscillatory and transient components. The corresponding optimization problem of MCA is resolved by the split augmented Lagrangian shrinkage algorithm (SALSA). The applications of the proposed method to speech, electroencephalo-graph (EEG), and electrocardiograph (ECG) signals are included.